Elliptic Curve Cryptography (ECC) has been gaining momentum as a replacement for RSA public key cryptography largely based on its efficiency, but also because the US National Security Agency (NSA) included it, while excluding RSA, from its Suite B cryptography recommendations. Suite B is a set of algorithms that the NSA recommends for use in protecting both classified and unclassified US government information and systems.
Public key cryptography is the basis for tools like ssh as well as Secure Sockets Layer (SSL) for encrypting web traffic. For readers who would like more information, a nice introduction to public key cryptography and the RSA algorithm can be found on Wikipedia.